Down two with one shot left
Your basketball team is losing by 2 points with time for one last shot.
- A three-pointer goes in with probability and wins the game.
- A two-pointer goes in with probability and sends the game to overtime, which you win with probability .
What is your probability of winning with the better choice?
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
Compare the two choices directly.
The two-pointer only gets you to overtime.
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s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. Compare the probability of winning with each shot.
Step 1: the three. You win with probability .
Step 2: the two. You need the shot and then overtime: .
Step 3. The two-pointer is slightly better: .
The point. The three-pointer looks attractive because it wins outright, but the overtime coin flip still leaves the two-pointer ahead. The decision flips if overtime is less favourable: with a winning chance below in overtime, go for three.